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Testing for ellipsoidal symmetry: A comparison study

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  • Sakhanenko, Lyudmila

Abstract

The focus of this paper is the methodology for testing ellipsoidal symmetry, which was recently proposed by Koltchinskii and Sakhanenko [Koltchinskii, V., Sakhanenko, L. 2000. Testing for ellipsoidal symmetry of a multivariate distribution. In: Giné, E., Mason, D., Wellner, J. (Eds.), High Dimensional Probability II. In: Progress in Probability, Birkhäuser, Boston, pp. 493-510]. It is a class of omnibus bootstrap tests that are affine invariant and consistent against any fixed alternative. First, we study their behavior under a sequence of local alternatives. Secondly, a finite sample comparison study of this new class of tests with other popular methods given by Beran, Manzotti et al., and Huffer et al. is carried out. We find that the new tests outperform other methods in preserving the level and have superior power for the most of the chosen alternatives. We also suggest a tool for identifying periods of financial instability and crises when these tests are applied to the distribution of the return rates of stock market indices. These tests can be used in place of tests for normality of asset return distributions since ellipsoidally symmetric distributions are the natural extensions of multivariate normal distributions, so that the capital asset pricing model holds.

Suggested Citation

  • Sakhanenko, Lyudmila, 2008. "Testing for ellipsoidal symmetry: A comparison study," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 565-581, December.
    • Handle: RePEc:eee:csdana:v:53:y:2008:i:2:p:565-581
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    References listed on IDEAS

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    1. Berk, Jonathan B., 1997. "Necessary Conditions for the CAPM," Journal of Economic Theory, Elsevier, vol. 73(1), pages 245-257, March.
    2. Huffer, Fred W. & Park, Cheolyong, 2007. "A test for elliptical symmetry," Journal of Multivariate Analysis, Elsevier, vol. 98(2), pages 256-281, February.
    3. Keith Vorkink & Douglas J. Hodgson & Oliver Linton, 2002. "Testing the capital asset pricing model efficiently under elliptical symmetry: a semiparametric approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(6), pages 617-639.
    4. Heathcote, C. R. & Rachev, S. T. & Cheng, B., 1995. "Testing Multivariate Symmetry," Journal of Multivariate Analysis, Elsevier, vol. 54(1), pages 91-112, July.
    5. Keith Vorkink, 2003. "Return Distributions and Improved Tests of Asset Pricing Models," The Review of Financial Studies, Society for Financial Studies, vol. 16(3), pages 845-874, July.
    6. Koltchinskii, V. I. & Li, Lang, 1998. "Testing for Spherical Symmetry of a Multivariate Distribution," Journal of Multivariate Analysis, Elsevier, vol. 65(2), pages 228-244, May.
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    Cited by:

    1. Ali Genç, 2013. "Moments of truncated normal/independent distributions," Statistical Papers, Springer, vol. 54(3), pages 741-764, August.
    2. Francq, C. & Jiménez-Gamero, M.D. & Meintanis, S.G., 2017. "Tests for conditional ellipticity in multivariate GARCH models," Journal of Econometrics, Elsevier, vol. 196(2), pages 305-319.
    3. Sladana Babic & Laetitia Gelbgras & Marc Hallin & Christophe Ley, 2019. "Optimal tests for elliptical symmetry: specified and unspecified location," Working Papers ECARES 2019-26, ULB -- Universite Libre de Bruxelles.
    4. Batsidis, Apostolos & Zografos, Konstantinos, 2013. "A necessary test of fit of specific elliptical distributions based on an estimator of Song’s measure," Journal of Multivariate Analysis, Elsevier, vol. 113(C), pages 91-105.
    5. Albisetti, Isaia & Balabdaoui, Fadoua & Holzmann, Hajo, 2020. "Testing for spherical and elliptical symmetry," Journal of Multivariate Analysis, Elsevier, vol. 180(C).

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